На основе математической модели случайных возмущений и математического описания задачи поиска экстремума унимодальной функции в условиях действия случайных возмущений сформулирована и описана математическая постановка задачи синтеза помехоустойчивых методов одномерного поиска в условиях действия случайных возмущений. The types of random perturbations and their manifes-tations, which allowed to mathematically describe random perturbations in the form of unipolar and bipolar sequence. On the basis of analyzing the general scheme of the onedimensional search of the extremum point unimodal function under the action of certain types of random perturbations describes the mathematical formulation of the problem of synthesis of noiseproof methods one-dimensional search under the action of random perturbations, which allows the development of search methods, which have given the best performance and noise stability.